What is the extreme f(x)=13x^3+138x^2-103 ?

The extreme f(x)=13x^3+138x^2-103 is Maximum(-92/13 , 371937/169),Minimum(0,-103)

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extreme f(x)=13x^3+138x^2-103

extreme points

f (x) = 13 x^{3} + 138 x^{2} - 103

Maximum (- \frac{92}{13}, \frac{371937}{169}), Minimum (0, - 103)

Solution steps

f^{'} (x) = 39 x^{2} + 276 x

Find intervals:

Increasing

: - \infty < x < - \frac{92}{13},

Decreasing

: - \frac{92}{13} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{92}{13}

into

13 x^{3} + 138 x^{2} - 103 : \frac{371937}{169}

Maximum (- \frac{92}{13}, \frac{371937}{169})

Plug

x = 0

into

13 x^{3} + 138 x^{2} - 103 : - 103

Minimum (0, - 103)

Maximum (- \frac{92}{13}, \frac{371937}{169}), Minimum (0, - 103)

What is the extreme f(x)=13x^3+138x^2-103 ?
The extreme f(x)=13x^3+138x^2-103 is Maximum(-92/13 , 371937/169),Minimum(0,-103)